338. Counting Bits

https://leetcode.com/problems/counting-bits/

Problem

Given a non-negative integer number num. For every number i in the range 0 ≤ i ≤ num calculate the number of 1's in their binary representation and return them as an array.

Example 1:

Input: 2
Output: [0,1,1]

Example 2:

Input: 5
Output: [0,1,1,2,1,2]

Follow up:

• It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n) /possibly in a single pass?

• Space complexity should be O(n).

• Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.

Solution

1. $O(N \times sizeof(integer))$

class Solution {
public:
    vector<int> countBits(const int num) {
        vector<int> counter;
        counter.reserve(num + 1);
        counter.push_back(0);
        for (int i = 1; i <= num; ++i) {
            int powerof2 = 1;
            while ((powerof2 << 1) <= i) powerof2 <<= 1;
            counter.push_back(counter[i - powerof2] + 1);
        }
        return counter;
    }
};

2. $O(N)$

class Solution {
public:
    vector<int> countBits(const int num) {
        vector<int> counter;
        counter.reserve(num + 1);
        counter.push_back(0);
        int powerof2 = 1;
        for (int i = 1; i <= num; ++i) {
            if ((powerof2 << 1) <= i) powerof2 <<= 1;
            counter.push_back(counter[i - powerof2] + 1);
        }
        return counter;
    }
};

• #bitwise